This is a competing renewal application for an Institutional Training Grant to support post-doctoral training in Computational Visual Neuroscience at the Center for Neural Science (CNS) and the Courant Institute for Mathematical Sciences (CIMS) at the Washington Square campus of New York University. The first funding period for this grant began in September 2001. Since inception this training grant has provided postdoctoral training in computational visual neuroscience at the Center for Neural Science (CNS) and the Courant Institute for Mathematical Sciences (CIMS) of New York University. We have trained junior scientists with backgrounds in the mathematical, computational, and physical sciences for research careers in visual neuroscience. This program is for postdoctoral fellows with appointments in CNS who will have research or thesis projects, respectively, under joint co-supervision by faculty members in CNS and CIMS. We will emphasize the bi-directional interaction between large-scale mathematical modeling and neurobiological experimentation, for instance the application of modern techniques for brain imaging (fMRI, optical imaging, electrical source imaging, and multi-unit recording). The Training Program will be founded upon our extensive experience at CNS and CIMS in interdisciplinary research and training. Special Features of the Program include: (i) hands on exposure to neuroscience research in laboratories of the Program's faculty;(ii) to provide a good working knowledge of mathematical and computational tools, and neuroscience;(iii) research experience as members of interdisciplinary research teams, with co-advisors from CNS and CIMS;(iv) weekly working group meetings during the academic year, to discuss ongoing research, theoretical issues, and techniques, as a vehicle for bridging the two cultures of mathematics and neuroscience;(v) excellent computational facilities located within CNS and CIMS;(vi) state-of-the-art brain imaging facilities in a new NYU Brain Imaging Center and in allied laboratories.